MinT - Best Known (48, 92, s)-Nets in Base 16

Best Known (48, 92, s)-Nets in Base 16

(48, 92, 518)-Net over F₁₆ — Constructive and digital

Digital (48, 92, 518)-net over F₁₆, using

trace code for nets [i] based on digital (2, 46, 259)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(48, 92, 642)-Net over F₁₆ — Digital

Digital (48, 92, 642)-net over F₁₆, using

trace code for nets [i] based on digital (2, 46, 321)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 320)-sequence over F₂₅₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 2 and N(F) ≥ 321, using
    - sharp bound on the number of rational points on curves with genus 2 [i]

(48, 92, 65477)-Net in Base 16 — Upper bound on s

There is no (48, 92, 65478)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 601 292728 255322 536163 701364 280842 152887 406426 636212 677231 613110 248917 725366 382315 540713 370242 680555 645495 645216 > 16⁹² [i]